Prime Numbers

I’ve been wondering why people think Prime numbers are so special. To me they are only an inconsistency within the logic of how Multiplication works, meaning all that Multiplication is, is a short form for Addition with the “Same Number!” An example:

(2 * 3) = (2 + 2 + 2) = 6

Again:

(3 * 7) = (3 + 3 + 3 + 3 + 3 + 3 + 3) = 21

It’s much easier and convenient to write:

(3 + 3 + 3 + 3 + 3 + 3 + 3 + 3 + 3 + 3) as (3 * 10) it’s easier to read and calculate.

Multiplication’s greatest strength is also its greatest weakness, which is the fact that it’s the Same Number being used again and again in the process Addition. Meaning the short from of (3 * 7) can be expressed in Addition as either (7 + 7 + 7) or (3 + 3 + 3 + 3 + 3 + 3 + 3). To me all that a Prime number is, is a number that has no short form! The short form of 6 is (3 * 2), the short from of 24 is either (2 * 12), (3 * 8), (4 * 6), etc. It’s because of the limits within Multiplication that it’s impossible to create 3 as the only numbers you can Multiply with are 1 and 2 with is (1 * 2) = 2 likewise you can’t make 2 from 1, (1 * 1) = 1, a problem that doesn’t exist when Addition is written in its long form.

This, to me, is an inconsistent property inherent in the logical formula of Multiplication. There are no such things as ‘Prime Numbers’ with addition, as all numbers come from 1 even the number 2 is just a short form of (1 + 1), 3 = (1 + 1 + 1), etc. So to then call numbers which have no short form in Multiplication ‘Primes’ seems to be giving them an importance that is only bestowed because of a fundamental weakness in Multiplication when dealing with Natural Numbers, seems illogical. I’m not saying this weakness doesn’t have its uses, cryptology being one of the most important from a world perspective. But this is a use that is possible because of the flawed nature of multiplication.

This is only a flaw in Multiplication, as Division can create any number. To create 7 we just do (21 / 3) = 7. Well you could say you’ve just created a Prime with the help of another Prime. Not true, 3 and 7 are Natural Numbers and only considered Primes because you can’t create them in Multiplication. In the first 10 numbers there are 5 Primes because of the limited number of Numbers available. Then the range 11 – 20 has 4, 21 – 30 and 31 – 40 each only have 2, as you obtain more numbers to Multiply with the frequency of Primes reduce. They don’t vanish completely as the fundamental flaw in Multiplication scales (or lessens depending on how you want to view it) with the number of Numbers available for its use.

So to sum it all up: Prime Numbers are only the correction to an Error inherent in Multiplication. While this error has its uses (cryptology) are these numbers really “Special” or just “Special” in relation to Multiplication?

Hmm, To me, numbers are a natural phenomenum.
I mean to say, they are not man made. Man has just given symbols to represent a ‘count’ of items.

Through observation and use man has stumbled upon peculiarities of the natural count of things…
That being Prime numbers and pi etc.

You call prime numbers an error of multiplication, which you could say(and I think you are saying) is a man made short version for natural addition.

Seeing that humans spend alot of their time preoccupied with seeking answers, it appears that any irregularity throws open more questions, and primes lead mathmaticians down a path that many have walked before, yet none have reached the end, the pot of gold, the Holy Grail.

Man is obsessed with discovering the meaning behind existence, whether we are aware of it or not. It is what drives research, learning and exploration. The need to know. To have a reason for it all.

So it seems they are to be labeled ‘special’ as their meaning is unknown, but offer a glimpse of the hidden, that the schizophrenic mind is so aware of, allways reaching for, but never quite unravelling.
We can feel the answer, we know instinctivly it is there, it calls to us all the time, yet with every step closer, every problem solved, a new riddle is lain before us…That to me is why Prime numbers are considered special, maybe this time, this is the key?

But as you imply, is multiplication natural or man made? Thus making Prime numbers man made also.

MentulZen.

Prime numbers are useful! That’s why we love them!

Think about it, a number that cannot be derived via division or multiplication!

The uses for prime numbers are amazing! Take for instance, in encryption. Any even number could result in a binary key search algorithm which runs at a speed of log2(N) efficiency (the best of the best). An odd number that is a multiple derivative is (I believe) subject to a SQRT(N) key search (still damn fast). However, with a prime number, you can garuntee that it would be a search of N at least.

Prime numbers are also important to patterns in sinusoids, development of unique polynomial derivatives, and various other cooky mathematical quirks and fun stuff.

There’s nothing freaky about prime numbers. They are the only “new” numbers in terms of multiplication.

If 7 wasn’t prime, 14 wouldn’t be divisible by two. Freaky way of thinking about it, but that’s just to help understand why they are neat…

They are the base numbers of all other numbers multiplication-wise.

They’re not “new” numbers, the quantity of 7 has always been 7. A prime number is defined by the fact it can’t be created by Multiplication. Multiplication is just a short form of Addition, but because of its limitations there are numbers that can’t be created. This error is then called ‘Prime’ as some how that number must be special. In effect there are wholes in the number line when Multiplication of whole numbers are used, which are filled by Prime numbers to correct that error. It’s this property of Multiplication that allows encryption, as once you multiply the two ‘Prime’ numbers together it’s like a one way HASH code, meaning you can’t get back to the two primes without Factoring the number created.

Haha, I have to disagree! Why wouldn’t 14 be divisible by 2??? Every number that is possible can be generated by a Division operation. Division and Multiplication work differently. Multiplication can’t create an answer that is 2, while Division can (8 / 4), (16 / 8), (30000 / 15000) etc, there are an infinite number of ways you can create an answer of 2 from a Division operation.

That’s not quite accurate. A Prime number is a number that can’t be generated by a Multiplication operation. So by definition any number that is not multipliable is a prime, because of this, it means that all other numbers must be a composite of any other prime number, otherwise it would become a prime its self. 1, 2, 3, 5, 7 are all primes, these are the basic seeds of the Multiplication numbers universe. Addition, Subtraction, and Division don’t need Primes. The concept of Primes wouldn’t exist if Multiplication also didn’t exist; it’s multiplication that gives Prime numbers their life.

Who first discovered prime numbers? Was it in Greece? When?

I hate to be a bastard about this one, but you might want to specify that a prime number can’t be created by the multiplication of rational numbers

Example: The number 3 is a prime number but…

sqrt(3) * sqrt(3) = 3

I happen to be very interested in Prime Numbers. You must know Pax that really big prime numbers are sometimes used in public key encryption and that there are many interesting theories, etc about prime numbers. For instance, there is no ‘greatest’ prime, because if you take all of the primes known and multiply them together and subtract one that number will either be a new prime or the product of unknown primes. Also one need test a number only up to its square root to find out if it is prime. That is one should divide the number by all of the primes up to the square root of the number being tested. Lesser known than this however is the fact that if the smallest divisor is greater than the cube root of the number being tested then the number in question is (if not prime) is the product of only two primes. The proof of this is quite simple. The least prime divisor is greater than x ^1/3 (read base x to the exponent 1/3) so the aliquot or other divisor is < x^2/3. If the aliquot divisor has a factor then, it must be less than the square root of x^2/3 or less than x^1/3 which contradicts the original thesis. Most new primes discovered are of the form of 2^x-1 after a man called Mersenne.

Haha, it has to be a whole number! That’s part of my point we can create any number we wish if we us fractional numbers or numbers with decimal places. But the rules for primes that they can’t be made our of interger numbers, i.e. thinks 1 2 … 1003 1004 etc. Except 1 and itself.

I know, that’s one of the reasons I became interested in Primes, as a way of breaking encryption. As all Public and Private keys are is a Large Prime multiple by another (well a best guess prime number). And because its still computationally very hard to factor such large numbers it becomes safer to do secure commutations this way.

I didn’t know this. I’ll have to read into this a little more. I have a book sitting on my bookshelf now for about 2 months called “The Magic of the Primes”, but I’ve yet to find the time to read it. But like 100 other books its next on my list.

I knew about this, you can download a program that’s like SETI in that fact that a group of computer users are trying to find the next largest prime and prove that it’s really. I think they found a new one about 6 months ago and it was massive. Basically that is the formal for all odd numbers that can ever exist.

When i was younger i avidly perused a book by Albert H. Beiler called recreations in the theory of numbers. It was very entertaining. I know this sounds weird, but my programmable calculator and i used to spend hours factoring numbers. I also used to come up with various formulae for the distribution of primes. I also have mathematics for the million by Hogben and some entertaining number theory books by Martin Gardner. The entertaining value of math is frequently overlooked.

I heard today there are perfect numbers!
6 28 496
are the only ones until 1000
I didn’t quite get the explanation, does anyone know what it means?

A perfect number is a number which is equal to the sum of all of it’s divisors excluding itself and takes the general form 2^n-1*2(n-1) where 2^n-1 is prime, thus
6 =2^2-1 (3)=1+2+3=6
28 =2^3-1 (7)=1+2+4+7+14
496
8128
33550336

That applies to even perfect numbers. What’s the current verdict on odd perfect numbers? Have they found any? Can they exist?

And if i were perfect i would always remember to log in…

It’s not too weird. I used to do the same thing. THough UI was most obsessed with dividing large numbers by 5 and 2, and seeng how many cycles it’d take to get me down closest to 2.

But Pax Vitae, I can’t possibly fathom your long opening post. Prime whole numbers are only divisble to other whole numbers by themselves and 1. That’s what makes them different from others. That’s the end of the story. I’ve never heard anyone gushing over how this condition is “so special.”

Did a mathematician hurt your heart or something? What gives?

to me, pax’s thesis is a ‘prime’ example of the exception proving the rule. Prime numbers allow us to further elucidate the characteristics of multiplication.

Further ‘compounding’ the multiplicity of mathematical problems and solutions, not to mention the problem of forgetting to log in…

random piece of useless info. i worked with an architect that showed me that if you order a load of numbers in a certain way (cant really remember how) then mark off the prime numbers it begins to forma shape which is one of the basic shapes in sacred geometry. Thought it was kinda interesting, the thought that they might have a bit more relevance than we usually grant them…at the same time time he told me the whole “bible predicting the future” which i dont really beleive in or at least think that it is pure chance…

If ya look up “spiral prime numbers” you start to get the idea, but this website should give the idea…really random i know!

fermi.franken.de/wschildbach/primes.html